
"""
    Copyright (C) <2010>  Autin L.
    
    This file ePMV_git/patch/spaceGroups.py is part of ePMV.

    ePMV is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    ePMV is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with ePMV.  If not, see <http://www.gnu.org/licenses/gpl-3.0.html>.
"""
# $Header: /opt/cvs/python/packages/share1.5/symserv/spaceGroups.py,v 1.1 2008/10/24 22:26:52 sargis Exp $
#
# $Id: spaceGroups.py,v 1.1 2008/10/24 22:26:52 sargis Exp $
#
spaceGroups = {
'P -1': [
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
        ], 
#_symmetry_equiv_pos_as_xyz
#    'x, y, z'
#    '-x, -y, -z'              
'P 1': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
        ],
'P 2': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
        ],
'P 21': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.500000, 0.000000) ), 
        ],
'C 2': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.500000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.500000, 0.500000, 0.000000) ), 
        ],
'P 2 2 2': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
        ],
'P 2 2 21': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.500000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.500000) ), 
        ],
'P 21 21 2': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.500000, 0.500000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.500000, 0.500000, 0.000000) ), 
        ],
'P 21 21 21': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.000000, 0.500000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.500000, 0.500000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.500000, 0.500000) ), 
        ],
#_symmetry_equiv_pos_as_xyz
#'x, y, z'
#'-x+1/2, -y, z+1/2'
#'x+1/2, -y+1/2, -z'
#'-x, y+1/2, -z+1/2'      
'C 2 2 21': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.500000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.500000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.500000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.500000, 0.500000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.500000, 0.500000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.500000, 0.500000, 0.500000) ), 
        ],
'C 2 2 2': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.500000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.500000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.500000, 0.500000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.500000, 0.500000, 0.000000) ), 
        ],
'F 2 2 2': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.500000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.500000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.500000, 0.500000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.500000, 0.500000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.500000, 0.500000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.500000, 0.500000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.500000, 0.500000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.500000, 0.500000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.000000, 0.500000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.000000, 0.500000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.500000, 0.000000, 0.500000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.500000, 0.000000, 0.500000) ), 
        ],
'I 2 2 2': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.500000, 0.500000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.500000, 0.500000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.500000, 0.500000, 0.500000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.500000, 0.500000, 0.500000) ), 
        ],
'I 21 21 21': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.000000, 0.500000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.500000, 0.500000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.500000, 0.500000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.500000, 0.500000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.500000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.500000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.500000, 0.000000, 0.000000) ), 
        ],
'P 4': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((0.000000, 1.000000, 0.000000), (-1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((0.000000, -1.000000, 0.000000), (1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
        ],
'P 41': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.500000) ), 
( ((0.000000, -1.000000, 0.000000), (1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.250000) ), 
( ((0.000000, 1.000000, 0.000000), (-1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.750000) ), 
        ],
'P 42': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((0.000000, -1.000000, 0.000000), (1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.500000) ), 
( ((0.000000, 1.000000, 0.000000), (-1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.500000) ), 
        ],
'P 43': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.500000) ), 
( ((0.000000, -1.000000, 0.000000), (1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.750000) ), 
( ((0.000000, 1.000000, 0.000000), (-1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.250000) ), 
        ],
'I 4': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((0.000000, 1.000000, 0.000000), (-1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((0.000000, -1.000000, 0.000000), (1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.500000, 0.500000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.500000, 0.500000) ), 
( ((0.000000, 1.000000, 0.000000), (-1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.500000, 0.500000) ), 
( ((0.000000, -1.000000, 0.000000), (1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.500000, 0.500000) ), 
        ],
'I 41': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((0.000000, -1.000000, 0.000000), (1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.500000, 0.250000) ), 
( ((0.000000, 1.000000, 0.000000), (-1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.500000, 0.250000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.500000, 0.500000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.500000, 0.500000) ), 
( ((0.000000, -1.000000, 0.000000), (1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.000000, 0.750000) ), 
( ((0.000000, 1.000000, 0.000000), (-1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.000000, 0.750000) ), 
        ],
'P 4 2 2': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((0.000000, -1.000000, 0.000000), (-1.000000, 0.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((0.000000, 1.000000, 0.000000), (1.000000, 0.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((0.000000, 1.000000, 0.000000), (-1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((0.000000, -1.000000, 0.000000), (1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
        ],
'P 4 21 2': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.500000, 0.500000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.500000, 0.500000, 0.000000) ), 
( ((0.000000, 1.000000, 0.000000), (1.000000, 0.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((0.000000, -1.000000, 0.000000), (-1.000000, 0.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((0.000000, 1.000000, 0.000000), (-1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.500000, 0.000000) ), 
( ((0.000000, -1.000000, 0.000000), (1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.500000, 0.500000, 0.000000) ), 
        ],
'P 41 2 2': [
( ((1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.500000) ), 
( ((0.000000, -1.000000, 0.000000), (1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.250000) ), 
( ((0.000000, 1.000000, 0.000000), (-1.000000, 0.000000, 0.000000), (0.000000, 0.000000, 1.000000)), (0.000000, 0.000000, 0.750000) ), 
( ((-1.000000, 0.000000, 0.000000), (0.000000, 1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.000000) ), 
( ((1.000000, 0.000000, 0.000000), (0.000000, -1.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.500000) ), 
( ((0.000000, -1.000000, 0.000000), (-1.000000, 0.000000, 0.000000), (0.000000, 0.000000, -1.000000)), (0.000000, 0.000000, 0.250000) ), 
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( ((0.000000, 0.000000, 1.000000), (0.000000, 1.000000, 0.000000), (-1.000000, 0.000000, 0.000000)), (0.500000, 0.500000, 0.000000) ), 
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'F D D D':[
([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [0.0, 0.0, 0.0]) ,
([[-1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, 1.0]], [0.0, 0.0, 0.0]) ,
([[-1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, -1.0]], [0.0, 0.0, 0.0]) ,
([[1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0]], [0.0, 0.0, 0.0]) ,
([[-1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0]], [0.25, 0.25, 0.25]) ,
([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, -1.0]], [0.25, 0.25, 0.25]) ,
([[1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, 1.0]], [0.25, 0.25, 0.25]) ,
([[-1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [0.25, 0.25, 0.25]) ,
([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [0.0, 0.5, 0.5]) ,
([[-1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, 1.0]], [0.0, 0.5, 0.5]) ,
([[-1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, -1.0]], [0.0, 0.5, 0.5]) ,
([[1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0]], [0.0, 0.5, 0.5]) ,
([[-1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0]], [0.25, 0.75, 0.75]) ,
([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, -1.0]], [0.25, 0.75, 0.75]) ,
([[1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, 1.0]], [0.25, 0.75, 0.75]) ,
([[-1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [0.25, 0.75, 0.75]) ,
([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [0.5, 0.0, 0.5]) ,
([[-1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, 1.0]], [0.5, 0.0, 0.5]) ,
([[-1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, -1.0]], [0.5, 0.0, 0.5]) ,
([[1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0]], [0.5, 0.0, 0.5]) ,
([[-1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0]], [0.75, 0.25, 0.75]) ,
([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, -1.0]], [0.75, 0.25, 0.75]) ,
([[1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, 1.0]], [0.75, 0.25, 0.75]) ,
([[-1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [0.75, 0.25, 0.75]) ,
([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [0.5, 0.5, 0.0]) ,
([[-1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, 1.0]], [0.5, 0.5, 0.0]) ,
([[-1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, -1.0]], [0.5, 0.5, 0.0]) ,
([[1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0]], [0.5, 0.5, 0.0]) ,
([[-1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0]], [0.75, 0.75, 0.25]) ,
([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, -1.0]], [0.75, 0.75, 0.25]) ,
([[1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, 1.0]], [0.75, 0.75, 0.25]) ,
([[-1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [0.75, 0.75, 0.25]) ,
],
'F D D D X' : [
(((1.000000, 0.000000, 0.000000), #1
   (0.000000, 1.000000, 0.000000), 
    (0.000000, 0.000000, 1.000000)), 
    (0.000000, 0.000000, 0.000000) ), 
(((-1.000000, 0.000000, 0.000000), #2
   (0.000000, -1.000000, 0.000000), 
    (0.000000, 0.000000, 1.000000)), 
    (3./4., 3./4., 0.000000) ), 
(((-1.000000, 0.000000, 0.000000), #3
   (0.000000, 1.000000, 0.000000), 
    (0.000000, 0.000000, -1.000000)), 
    (3./4., 0.000000, 3./4.) ), 
(((1.000000, 0.000000, 0.000000), #4
   (0.000000, -1.000000, 0.000000), 
    (0.000000, 0.000000, -1.000000)), 
    (0.000000, 3./4., 3./4.) ), 
(((-1.000000, 0.000000, 0.000000), #5
   (0.000000, -1.000000, 0.000000), 
    (0.000000, 0.000000, -1.000000)), 
    (0.000000, 0.000000, 0.000000) ), 
(((1.000000, 0.000000, 0.000000), #6
   (0.000000, 1.000000, 0.000000), 
    (0.000000, 0.000000, -1.000000)), 
    (1./4., 1./4., 0.000000) ), 
(((1.000000, 0.000000, 0.000000), #7
   (0.000000, -1.000000, 0.000000), 
    (0.000000, 0.000000, 1.000000)), 
    (1./4., 0.000000, 1./4.) ), 
(((-1.000000, 0.000000, 0.000000), #8
   (0.000000, 1.000000, 0.000000), 
    (0.000000, 0.000000, 1.000000)), 
    (0.000000, 1./4., 1./4.) ), 
(((1.000000, 0.000000, 0.000000), #9
   (0.000000, 1.000000, 0.000000), 
    (0.000000, 0.000000, 1.000000)), 
    (0.000000, 1./2., 1./2.) ), 
(((-1.000000, 0.000000, 0.000000), #10
   (0.000000, -1.000000, 0.000000), 
    (0.000000, 0.000000, 1.000000)), 
    (3./4., 1./4., 1/2.) ), 
(((-1.000000, 0.000000, 0.000000),#11 
   (0.000000, 1.000000, 0.000000), 
    (0.000000, 0.000000, -1.000000)), 
    (3./4., 1./2., 1./4.) ), 
(((1.000000, 0.000000, 0.000000), #12
   (0.000000, -1.000000, 0.000000), 
    (0.000000, 0.000000, -1.000000)), 
    (0.000000, 1./4., 1./4.) ), 
(((-1.000000, 0.000000, 0.000000), #13
   (0.000000, -1.000000, 0.000000), 
    (0.000000, 0.000000, -1.000000)), 
    (0.000000, 1./2., 1./2.) ), 
(((1.000000, 0.000000, 0.000000), #14
   (0.000000, 1.000000, 0.000000), 
    (0.000000, 0.000000, -1.000000)), 
    (1./4., 3./4., 1./2.) ), 
(((1.000000, 0.000000, 0.000000), #15
   (0.000000, -1.000000, 0.000000), 
    (0.000000, 0.000000, 1.000000)), 
    (1./4., 1./2., 3/4.) ), 
(((-1.000000, 0.000000, 0.000000),#16 
   (0.000000, 1.000000, 0.000000), 
    (0.000000, 0.000000, 1.000000)), 
    (0.000000, 3/4., 3/4.) ), 
(((1.000000, 0.000000, 0.000000), #17
   (0.000000, 1.000000, 0.000000), 
    (0.000000, 0.000000, 1.000000)), 
    (1./2, 0.000000, 1./2) ), 
(((-1.000000, 0.000000, 0.000000), #18
   (0.000000, -1.000000, 0.000000), 
    (0.000000, 0.000000, 1.000000)), 
    (1./4, 3./4, 1./2) ), 
(((-1.000000, 0.000000, 0.000000), #19
   (0.000000, 1.000000, 0.000000), 
    (0.000000, 0.000000, -1.000000)), 
    (1./4, 0.000000, 1./4) ), 
(((1.000000, 0.000000, 0.000000), #20
   (0.000000, -1.000000, 0.000000), 
    (0.000000, 0.000000, -1.000000)), 
    (1./2, 3./4,1./4) ), 
(((-1.000000, 0.000000, 0.000000), #21
   (0.000000, -1.000000, 0.000000), 
    (0.000000, 0.000000, -1.000000)), 
    (1./2, 0.000000, 1./2) ), 
(((1.000000, 0.000000, 0.000000), #22
   (0.000000, 1.000000, 0.000000), 
    (0.000000, 0.000000, -1.000000)), 
    (3./4, 1./4, 1./2) ), 
(((1.000000, 0.000000, 0.000000), #23
   (0.000000, -1.000000, 0.000000), 
    (0.000000, 0.000000, 1.000000)), 
    (3./4, 0.000000, 3./4) ), 
(((-1.000000, 0.000000, 0.000000), #24
   (0.000000, 1.000000, 0.000000), 
    (0.000000, 0.000000, 1.000000)), 
    (1/2., 1/4., 3/4.) ), 
(((1.000000, 0.000000, 0.000000), #25
   (0.000000, 1.000000, 0.000000), 
    (0.000000, 0.000000, 1.000000)), 
    (1/2., 1/2., 0.000000) ), 
(((-1.000000, 0.000000, 0.000000),#26 
   (0.000000, -1.000000, 0.000000), 
    (0.000000, 0.000000, 1.000000)), 
    (1/4., 1/4., 0.000000) ), 
(((-1.000000, 0.000000, 0.000000), #27
   (0.000000, 1.000000, 0.000000), 
    (0.000000, 0.000000, -1.000000)), 
    (1/4., 1/2., 3/4.) ), 
(((1.000000, 0.000000, 0.000000), #28
   (0.000000, -1.000000, 0.000000), 
    (0.000000, 0.000000, -1.000000)), 
    (1/2., 1/4., 3/4.) ), 
(((-1.000000, 0.000000, 0.000000), #29
   (0.000000, -1.000000, 0.000000), 
    (0.000000, 0.000000, -1.000000)), 
    (1/2., 1/2., 0.000000) ), 
(((1.000000, 0.000000, 0.000000), #30
   (0.000000, 1.000000, 0.000000), 
    (0.000000, 0.000000, -1.000000)), 
    (3/4.,3/4., 0.000000) ), 
(((1.000000, 0.000000, 0.000000), #31
   (0.000000, -1.000000, 0.000000), 
    (0.000000, 0.000000, 1.000000)), 
    (3/4., 1/2., 1/4.) ), 
(((-1.000000, 0.000000, 0.000000), #32
   (0.000000, 1.000000, 0.000000), 
    (0.000000, 0.000000, 1.000000)), 
    (1/2., 3/4.,  1/4.) )  
],
} # end of spacegroupsdict
